## Vector Force Diagrams

Apparatus:

3 x 100g mass sets, 1 x unknown mass (M), 1 x force board, protractor, chalk, string, scissors,

access to a top-pan balance.

Diagrams:

Procedure:

1. Set up the apparatus as shown in diagram A.

2. Place three 100g masses in each of the holders (of mass 100g) and adjust the holdersâ€™ positions until equilibrium is obtained.

Note: To check that equilibrium has been obtained; displace one of the holders slightly, the system should return to its original position if it was in equilibrium.

3. Using the chalk, note the positions of the strings on the blackboard.

4. Using the information from the blackboard , construct a parallelogram of vectors diagram using the two outer masses as forcesandRemember that a mass of 100g will have a weight of 0.98 N.

Your diagram should look like diagram B. It should be drawn to scale and have the same angles as on the blackboard set-up. It should also be as large as possible.

5. Measure the length of the diagonal and so calculate the value of the resultant force

6. Compare the value ofobtained from your diagram with the actual value of

E.g. if you have used a total mass of 400g for weightshould be (4 x 0.98N) = 3.92N

7. Repeat steps 2 to 5 but with different masses in the holders (about three more combinations should be sufficient). Note you will probably have to keep the two outer weights similar to each other.

8. Finally replace the central mass holder with the unknown mass, markedRepeat as before, and so calculate values for the weight and mass of

9. By considering the accuracy of your first four diagrams estimate the uncertainties in your weight and mass values for

10. Use the top-pan balance to measure the mass ofand compare it with your experimental value!